WO01/5268A1 relates to a method for estimating the position and trajectory of a drill during drilling of boreholes in rock. WO01/75268A1 presents an adaptation to drill positioning of a method used for determining the relative position of similar microearthquake events described in Geophys. J. Int. (1995), 123, 409-419, by Slunga, Rögavaldsson and Bödvarsson. The method in WO01/75268A1 comprises the steps of determining the starting position of the drill bit and recording the received transient seismic waves generated by the drill on impact, and estimating the difference in arrival time between events. Using these estimations, the relative distances between the positions of the drill bit at different events are calculated and from these the present position is calculated.
The method described in WO01/75268A1 is particularly suitable when the length of the bore hole to be drilled is limited. However, when the drilling process reaches further, the properties in the rock may have changed considerably, in turn changing the propagation velocities of the seismic waves generated by the drill bit. Further, these changes are impossible to predict. Also, the propagation velocity differences may increase further by other discontinuities in the rock, such as cracks.
More particularly, in the method described in WO01/75268A1, the result is obtained by making the assumption that the propagation velocity in the rock in which drilling is performed is the same at two consecutive events. When only studying relative time differences between two events, errors due to varying properties in the rock are eliminated, or at least negligible, if these properties can be considered to be constant between the events, which is likely if the distance between the drill bit and a geophone is considerably longer than the distance between the position of the drill bit at the most recent event and the position of the drill bit at the current event. If the distance between the drill bit and a geophone is in the order of at least 102 times the distance traveled by the drill bit between the events, or more, errors due to varying properties in the rock are negligible. Thereby, the angular difference between the two signals is so small, that the two signals can be considered to propagate almost the same way through the rock towards a specific geophone, and thus through the same discontinuities in the rock. As a result, the difference in propagation velocity, and the corresponding arrival time difference would nearly or completely cancel.
The method described in WO01/75268A1 is particularly suitable when the length of the bore hole to be drilled is limited. FIG. 4 shows a rock drilling of a bore hole 10 in progress. During the drilling, the position of the drill bit 11 is calculated using transient seismic waves received by number of geophones, of which four is shown, 12a, 12b, 12c and 12d. It is to be understood, however, that in normal conditions, more than four geophones, e.g. 8 or more geophones, should be used since signals from one or more geophones usually is disturbed. When the drilling has reached a first location A1, in which a positioning of the drill bit is performed, the transient seismic wave generated by an event at the drill bit propagates along the path a, towards the geophone 12d. When the drill bit has reached a little bit further down the hole and its position again is about to be measured, at position A2, the transient seismic wave propagates along the path a2 towards the geophone 12d. The distance between the positions A1 and A2 is small, e.g. in the order of 0.25 m or 1 m, while the distance between A1 and 12d, and the distance between A2 and 12d may be 100 m or more. Accordingly, it can be understood that differences between propagation velocities along the paths a1 and a2 can be considered to be the same. As an example, the position of the drill bit may be calculated every 15 s or every minute, e.g. when an exemplary drilling process has reached a further 0.25 m or 1 m, respectively.
However, when the drilling process has reached further, e.g. to a location B1, the properties in the rock may have changed considerably. The distance between the positions A1 (A2) and B1 may be in the order 500 m or more, e.g. 1000-5000 m. In this case, the transient seismic wave generated by an event at the drill bit at B1 propagates along the path b1 towards the geophone 12d. When, as described above, the drill bit has reached a little bit further down the hole and its position is again about to be measured at position B2, the transient seismic wave propagates along the path b2 towards the geophone 12d. As easily can be understood, as the distance between the positions B1 and B2 still is equally small, and the distance between B1 (B2) and 12d now is considerably longer, the differences between the propagation velocities along the paths b1 and b2 is even smaller and thus even more likely to be the same or almost the same.
However, even if the propagation velocities of two consecutive measurements, such as A1-A2 or B1-B2 can be considered to be the same, the same assumption is not likely to be true regarding paths a1 (a2) and b1 (b2) owing to a number of reasons. Firstly, when drilling very deep bore holes, such as when drilling for oil or natural gas, the nature of the rock may change considerably as the drilling proceeds. Further, these changes are impossible to predict. This is exemplified in FIG. 4 where the line C represents a transition from one kind of rock to another, wherein the nature of the rock C1 above the line C may have a propagation velocity that differs substantially from the propagation velocity in the rock below the line C. Thus, if the propagation velocities along a1 and b1 (and along corresponding paths towards the other geophones) would be considered to be the same, the resulting calculated position of the drill bit may, instead of being calculated as the correct position B1, instead be calculated to be the position indicated by B1′, which may differ substantially from the position B1. Further, the propagation velocity differences between paths a1 and b1 may increase further by other discontinuities in the rock, such as cracks 13, 14. Even further, the propagation velocity varies with the increase in rock pressure and temperature as the drilling propagates further in depth. As is appreciated by a person skilled in the art, the above applies equally well to the other geophones 12a-c. 